I have a fountain pen that I've used on and off. Once you get used to writing with one, it's a pleasant experience, as they're smoother, and the shape of the nib makes your handwriting look nicer because it accentuates the difference between thick and thin parts of the letters, even in print (I rarely write in cursive with mine). It's also nice that, instead of just throwing it away when it dries out, you can refill it with whichever color of ink you like (when you like how a pen writes, it's always a bummer when you use it up and have to throw it away).
The downside of fountain pens, in my experience, is that their ink doesn't play well with cheap paper (which unfortunately includes most typical printer paper). It tends to get sucked along the paper fibers through capillary action, called "feathering" by fountain pen enthusiasts. There are special inks, like Noodler's X-Feather ink, that try to reduce this, though they don't eliminate it entirely. Fountain pen ink also takes longer to dry than ballpoint ink, meaning it's very easy to smudge the ink if you're not careful. I'd imagine left-handed people would find them almost unusable without having to relearn how to hold the pen to prevent this.